ADI spectral collocation methods for parabolic problems
We discuss the Crank–Nicolson and Laplace modified alternating direction implicit Legendre and Chebyshev spectral collocation methods for a linear, variable coefficient, parabolic initial-boundary value problem on a rectangular domain with the solution subject to non-zero Dirichlet boundary conditio...
Saved in:
| Published in | Journal of computational physics Vol. 229; no. 13; pp. 5182 - 5193 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Kidlington
Elsevier Inc
01.07.2010
Elsevier |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0021-9991 1090-2716 |
| DOI | 10.1016/j.jcp.2010.03.033 |
Cover
| Abstract | We discuss the Crank–Nicolson and Laplace modified alternating direction implicit Legendre and Chebyshev spectral collocation methods for a linear, variable coefficient, parabolic initial-boundary value problem on a rectangular domain with the solution subject to non-zero Dirichlet boundary conditions. The discretization of the problems by the above methods yields matrices which possess banded structures. This along with the use of fast Fourier transforms makes the cost of one step of each of the Chebyshev spectral collocation methods proportional, except for a logarithmic term, to the number of the unknowns. We present the convergence analysis for the Legendre spectral collocation methods in the special case of the heat equation. Using numerical tests, we demonstrate the second order accuracy in time of the Chebyshev spectral collocation methods for general linear variable coefficient parabolic problems. |
|---|---|
| AbstractList | We discuss the Crank-Nicolson and Laplace modified alternating direction implicit Legendre and Chebyshev spectral collocation methods for a linear, variable coefficient, parabolic initial-boundary value problem on a rectangular domain with the solution subject to non-zero Dirichlet boundary conditions. The discretization of the problems by the above methods yields matrices which possess banded structures. This along with the use of fast Fourier transforms makes the cost of one step of each of the Chebyshev spectral collocation methods proportional, except for a logarithmic term, to the number of the unknowns. We present the convergence analysis for the Legendre spectral collocation methods in the special case of the heat equation. Using numerical tests, we demonstrate the second order accuracy in time of the Chebyshev spectral collocation methods for general linear variable coefficient parabolic problems. |
| Author | Bialecki, B. de Frutos, J. |
| Author_xml | – sequence: 1 givenname: B. surname: Bialecki fullname: Bialecki, B. email: bbialeck@mines.edu organization: Department of Mathematical and Computer Sciences, Colorado School of Mines, Golden, CO 80401, United States – sequence: 2 givenname: J. surname: de Frutos fullname: de Frutos, J. email: frutos@mac.uva.es organization: Departamento Matematica Applicada, Universidad de Valladolid, 47005 Valladolid, Spain |
| BackLink | http://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=22798791$$DView record in Pascal Francis |
| BookMark | eNp9kE1LAzEQhoNUsH78AG97EU9bJ8luk8WT-A0FL3oO2dkppqSbNVkF_72pLR48FAaGYZ53Bp5jNulDT4ydc5hx4POr1WyFw0xAnkHmkgdsyqGBUig-n7ApgOBl0zT8iB2ntAIAXVd6ytTN3XORBsIxWl9g8D6gHV3oizWN76FLxTLEYrDRtsE7LIYYWk_rdMoOl9YnOtv1E_b2cP96-1QuXh6fb28WJcq6GctWU2sJpepQ6KrSopWoWlFr0QluW6m1bYmLCqhCWwlAgdipaq4oL1CDPGGX27v58ccnpdGsXULy3vYUPpNRtVS1gEZm8mJH2oTWL6Pt0SUzRLe28dsIoRqtGp45vuUwhpQiLf8QDmbj0qxMdmk2Lg3IXJvb6l8G3firKWtzfm_yepukLOnLUTQJHfVInYtZuumC25P-AYLJj-s |
| CODEN | JCTPAH |
| CitedBy_id | crossref_primary_10_1016_j_jcp_2012_04_001 crossref_primary_10_1186_s13662_018_1825_2 |
| Cites_doi | 10.1090/S0025-5718-1993-1176704-7 10.1137/0103003 10.1090/S0025-5718-1989-0969489-7 10.1137/0907058 10.1023/B:NUMA.0000040056.52424.49 10.1016/j.cam.2005.05.020 10.1137/S0036142997310387 10.1137/0913035 10.1137/0707048 10.1137/0716039 10.1137/0712042 10.1016/S1570-8659(05)80035-3 10.1016/j.jcp.2008.06.009 10.1090/S0025-5718-04-01660-6 10.1137/0915089 10.1137/050627885 |
| ContentType | Journal Article |
| Copyright | 2010 Elsevier Inc. 2015 INIST-CNRS |
| Copyright_xml | – notice: 2010 Elsevier Inc. – notice: 2015 INIST-CNRS |
| DBID | AAYXX CITATION IQODW 7SC 7SP 7U5 8FD JQ2 L7M L~C L~D |
| DOI | 10.1016/j.jcp.2010.03.033 |
| DatabaseName | CrossRef Pascal-Francis Computer and Information Systems Abstracts Electronics & Communications Abstracts Solid State and Superconductivity Abstracts Technology Research Database ProQuest Computer Science Collection Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Academic Computer and Information Systems Abstracts Professional |
| DatabaseTitle | CrossRef Technology Research Database Computer and Information Systems Abstracts – Academic Electronics & Communications Abstracts ProQuest Computer Science Collection Computer and Information Systems Abstracts Solid State and Superconductivity Abstracts Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Professional |
| DatabaseTitleList | Technology Research Database |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Applied Sciences Physics |
| EISSN | 1090-2716 |
| EndPage | 5193 |
| ExternalDocumentID | 22798791 10_1016_j_jcp_2010_03_033 S002199911000152X |
| GroupedDBID | --K --M -~X .~1 0R~ 1B1 1RT 1~. 1~5 29K 4.4 457 4G. 5GY 5VS 6OB 6TJ 7-5 71M 8P~ 8WZ 9JN A6W AABNK AACTN AAEDT AAEDW AAIAV AAIKJ AAKOC AALRI AAOAW AAQFI AAQXK AAXUO AAYFN ABBOA ABFNM ABFRF ABJNI ABMAC ABNEU ABTAH ABXDB ABYKQ ACBEA ACDAQ ACFVG ACGFO ACGFS ACNCT ACNNM ACRLP ACZNC ADBBV ADEZE ADFGL ADIYS ADJOM ADMUD AEBSH AEFWE AEKER AENEX AFFNX AFKWA AFTJW AGHFR AGUBO AGYEJ AHHHB AHZHX AIALX AIEXJ AIKHN AITUG AIVDX AJBFU AJOXV ALMA_UNASSIGNED_HOLDINGS AMFUW AMRAJ AOUOD ASPBG AVWKF AXJTR AZFZN BBWZM BKOJK BLXMC CAG COF CS3 D-I DM4 DU5 EBS EFBJH EFLBG EJD EO8 EO9 EP2 EP3 F5P FDB FEDTE FGOYB FIRID FNPLU FYGXN G-2 G-Q GBLVA GBOLZ HLZ HME HMV HVGLF HZ~ IHE J1W K-O KOM LG5 LX9 LZ4 M37 M41 MO0 N9A NDZJH O-L O9- OAUVE OGIMB OZT P-8 P-9 P2P PC. Q38 R2- RIG RNS ROL RPZ SBC SDF SDG SDP SES SEW SHN SPC SPCBC SPD SPG SSQ SSV SSZ T5K T9H TN5 UPT UQL WUQ XFK YQT ZMT ZU3 ZY4 ~02 ~G- AATTM AAXKI AAYWO AAYXX ABWVN ACLOT ACRPL ACVFH ADCNI ADNMO AEIPS AEUPX AFJKZ AFPUW AGQPQ AIGII AIIUN AKBMS AKRWK AKYEP ANKPU APXCP CITATION EFKBS ~HD AFXIZ AGCQF AGRNS BNPGV IQODW SSH 7SC 7SP 7U5 8FD JQ2 L7M L~C L~D |
| ID | FETCH-LOGICAL-c359t-b8ebaec37dc284482b3c7b2582d21ab388abe1240e4ca420c2ccd7467e8abc803 |
| IEDL.DBID | AIKHN |
| ISSN | 0021-9991 |
| IngestDate | Mon Sep 29 05:08:29 EDT 2025 Mon Jul 21 09:14:12 EDT 2025 Wed Oct 01 05:12:29 EDT 2025 Thu Apr 24 23:05:26 EDT 2025 Fri Feb 23 02:29:11 EST 2024 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 13 |
| Keywords | Crank–Nicolson Legendre and Chebyshev polynomials Parabolic initial-boundary value problems Spectral collocation ADI Laplace modified Second order Band structure Spectral method Heat equation Chebyshev polynomial Boundary conditions Calculation methods Crank-Nicolson Fast Fourier transforms Discretization Dirichlet problem Boundary-value problems Initial value problems Calculation Legendre polynomials |
| Language | English |
| License | https://www.elsevier.com/tdm/userlicense/1.0 CC BY 4.0 |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c359t-b8ebaec37dc284482b3c7b2582d21ab388abe1240e4ca420c2ccd7467e8abc803 |
| Notes | ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 23 |
| PQID | 753752093 |
| PQPubID | 23500 |
| PageCount | 12 |
| ParticipantIDs | proquest_miscellaneous_753752093 pascalfrancis_primary_22798791 crossref_primary_10_1016_j_jcp_2010_03_033 crossref_citationtrail_10_1016_j_jcp_2010_03_033 elsevier_sciencedirect_doi_10_1016_j_jcp_2010_03_033 |
| ProviderPackageCode | CITATION AAYXX |
| PublicationCentury | 2000 |
| PublicationDate | 2010-07-01 |
| PublicationDateYYYYMMDD | 2010-07-01 |
| PublicationDate_xml | – month: 07 year: 2010 text: 2010-07-01 day: 01 |
| PublicationDecade | 2010 |
| PublicationPlace | Kidlington |
| PublicationPlace_xml | – name: Kidlington |
| PublicationTitle | Journal of computational physics |
| PublicationYear | 2010 |
| Publisher | Elsevier Inc Elsevier |
| Publisher_xml | – name: Elsevier Inc – name: Elsevier |
| References | Bialecki, Fernandes (bib4) 1999; 36 Fairweather (bib12) 1978; vol. 34 Bialecki, Karageorghis (bib7) 2008; 227 Bernardi, Maday (bib2) 1997; vol. V Marchuck (bib16) 1990 Bialecki, Fernandes (bib5) 2006; 28 B. Bialecki, A. Karageorghis, Spectral Chebyshev collocation for Poisson and biharmonic equations, submitted for publication. Strikwerda (bib22) 1989 Swarztrauber (bib23) 1985 Hundsdorfer, Verwer (bib14) 1989; 53 Samarskii (bib20) 2001 Peaceman, Rachford (bib17) 1955; 3 Bialecki, Karageorghis (bib6) 2004; 36 Jorge (bib15) 2006; 189 Dendy (bib9) 1975; 12 van der Vorst (bib24) 1992; 13 Shen (bib21) 1994; 15 Saad, Scultz (bib19) 1986; 7 Hundsdorfer, Verwer (bib13) 2003 Bialecki, Fernandes (bib3) 1995; 60 Alonso-Mallo, Cano, Jorge (bib1) 2004; 73 Douglas, Dupont, Ewing (bib11) 1979; 16 Douglas, Dupont (bib10) 1970; 7 Quarteroni, Valli (bib18) 1994 Alonso-Mallo (10.1016/j.jcp.2010.03.033_bib1) 2004; 73 Fairweather (10.1016/j.jcp.2010.03.033_bib12) 1978; vol. 34 Bialecki (10.1016/j.jcp.2010.03.033_bib3) 1995; 60 van der Vorst (10.1016/j.jcp.2010.03.033_bib24) 1992; 13 Quarteroni (10.1016/j.jcp.2010.03.033_bib18) 1994 Hundsdorfer (10.1016/j.jcp.2010.03.033_bib13) 2003 Bialecki (10.1016/j.jcp.2010.03.033_bib6) 2004; 36 Shen (10.1016/j.jcp.2010.03.033_bib21) 1994; 15 Strikwerda (10.1016/j.jcp.2010.03.033_bib22) 1989 Douglas (10.1016/j.jcp.2010.03.033_bib10) 1970; 7 Bialecki (10.1016/j.jcp.2010.03.033_bib7) 2008; 227 Peaceman (10.1016/j.jcp.2010.03.033_bib17) 1955; 3 Dendy (10.1016/j.jcp.2010.03.033_bib9) 1975; 12 Bialecki (10.1016/j.jcp.2010.03.033_bib4) 1999; 36 Saad (10.1016/j.jcp.2010.03.033_bib19) 1986; 7 Bernardi (10.1016/j.jcp.2010.03.033_bib2) 1997; vol. V Marchuck (10.1016/j.jcp.2010.03.033_bib16) 1990 10.1016/j.jcp.2010.03.033_bib8 Jorge (10.1016/j.jcp.2010.03.033_bib15) 2006; 189 Bialecki (10.1016/j.jcp.2010.03.033_bib5) 2006; 28 Samarskii (10.1016/j.jcp.2010.03.033_bib20) 2001 Hundsdorfer (10.1016/j.jcp.2010.03.033_bib14) 1989; 53 Douglas (10.1016/j.jcp.2010.03.033_bib11) 1979; 16 Swarztrauber (10.1016/j.jcp.2010.03.033_bib23) 1985 |
| References_xml | – volume: 28 start-page: 1054 year: 2006 end-page: 1077 ident: bib5 article-title: An alternating-direction implicit orthogonal spline collocation scheme for nonlinear parabolic problems on rectangular polygons publication-title: SIAM J. Sci. Comput. – year: 1985 ident: bib23 article-title: FFTPACK – volume: 227 start-page: 8588 year: 2008 end-page: 8603 ident: bib7 article-title: Spectral Chebyshev–Fourier collocation for the Helmholtz and variable coefficient equations in a disk publication-title: J. Comput. Phys. – volume: 15 start-page: 1489 year: 1994 end-page: 1505 ident: bib21 article-title: Efficient spectral-Galerkin method I. Direct solvers of second- and fourth-order equations using Legendre polynomials publication-title: SIAM J. Sci. Comput. – volume: 3 start-page: 28 year: 1955 end-page: 41 ident: bib17 article-title: The numerical solution of parabolic and elliptic differential equations publication-title: J. Soc. Indust. Appl. Math. – start-page: 197 year: 1990 end-page: 462 ident: bib16 article-title: Splitting and alternating direction methods publication-title: Handbook of Numerical Analysis, I – year: 1989 ident: bib22 article-title: Finite Difference Schemes for Partial Differential Equations – volume: 36 start-page: 1414 year: 1999 end-page: 1434 ident: bib4 article-title: An orthogonal spline collocation alternating direction implicit Crank–Nicolson method for linear parabolic problems on rectangles publication-title: SIAM J. Numer. Anal. – volume: 53 start-page: 81 year: 1989 end-page: 101 ident: bib14 article-title: Stability and convergence of the Peaceman–Rachford ADI method for initial-boundary value problems publication-title: Math. Comput. – reference: B. Bialecki, A. Karageorghis, Spectral Chebyshev collocation for Poisson and biharmonic equations, submitted for publication. – volume: 73 start-page: 1801 year: 2004 end-page: 1825 ident: bib1 article-title: Spectral-fractional step Runge–Kutta discretizations for initial boundary value problems with time dependent boundary conditions publication-title: Math. Comput. – volume: 36 start-page: 203 year: 2004 end-page: 227 ident: bib6 article-title: Legendre Gauss spectral collocation for the Helmholtz equation on a rectangle publication-title: Numer. Algorithms – volume: vol. 34 year: 1978 ident: bib12 article-title: Finite Element Galerkin Methods for Differential Equations publication-title: Lecture Notes in Pure and Applied Mathematics – year: 1994 ident: bib18 article-title: Numerical Approximation of Partial Differential Equations – volume: 7 start-page: 856 year: 1986 end-page: 869 ident: bib19 article-title: GMRES: a generalized minimal residual algorithm for solving non-symmetric linear systems publication-title: SIAM J. Sci. Stat. Comput. – volume: 7 start-page: 575 year: 1970 end-page: 626 ident: bib10 article-title: Galerkin methods for parabolic equations publication-title: SIAM J. Numer. Anal. – volume: 60 start-page: 545 year: 1995 end-page: 573 ident: bib3 article-title: Orthogonal spline collocation Laplace-modified and alternating direction methods for parabolic problems on rectangles publication-title: Math. Comput. – volume: 12 start-page: 541 year: 1975 end-page: 565 ident: bib9 article-title: An analysis of some Galerkin schemes for the solution of nonlinear time-dependent problems publication-title: SIAM J. Numer. Anal. – volume: 189 start-page: 676 year: 2006 end-page: 688 ident: bib15 article-title: A generalization of Peaceman–Rachford fractional step method publication-title: J. Comput. Appl. Math. – volume: 16 start-page: 503 year: 1979 end-page: 522 ident: bib11 article-title: Incomplete iterations for time-stepping a Galerkin method for a quasilinear parabolic problem publication-title: SIAM J. Numer. Anal. – volume: vol. V year: 1997 ident: bib2 article-title: Spectral Methods publication-title: Handbook of Numerical Analysis – year: 2001 ident: bib20 article-title: Theory of Difference Schemes – volume: 13 start-page: 631 year: 1992 end-page: 644 ident: bib24 article-title: BI-CGSTAB: a fast and smoothly converging variant of BI-CG for the solution of nonsymmetric linear systems publication-title: SIAM J. Sci. Stat. Comput. – year: 2003 ident: bib13 article-title: Numerical Solution of Time-Dependent Advection–Diffusion–Reaction Equations – volume: 60 start-page: 545 year: 1995 ident: 10.1016/j.jcp.2010.03.033_bib3 article-title: Orthogonal spline collocation Laplace-modified and alternating direction methods for parabolic problems on rectangles publication-title: Math. Comput. doi: 10.1090/S0025-5718-1993-1176704-7 – volume: 3 start-page: 28 year: 1955 ident: 10.1016/j.jcp.2010.03.033_bib17 article-title: The numerical solution of parabolic and elliptic differential equations publication-title: J. Soc. Indust. Appl. Math. doi: 10.1137/0103003 – volume: 53 start-page: 81 year: 1989 ident: 10.1016/j.jcp.2010.03.033_bib14 article-title: Stability and convergence of the Peaceman–Rachford ADI method for initial-boundary value problems publication-title: Math. Comput. doi: 10.1090/S0025-5718-1989-0969489-7 – volume: vol. 34 year: 1978 ident: 10.1016/j.jcp.2010.03.033_bib12 article-title: Finite Element Galerkin Methods for Differential Equations – volume: 7 start-page: 856 year: 1986 ident: 10.1016/j.jcp.2010.03.033_bib19 article-title: GMRES: a generalized minimal residual algorithm for solving non-symmetric linear systems publication-title: SIAM J. Sci. Stat. Comput. doi: 10.1137/0907058 – volume: 36 start-page: 203 year: 2004 ident: 10.1016/j.jcp.2010.03.033_bib6 article-title: Legendre Gauss spectral collocation for the Helmholtz equation on a rectangle publication-title: Numer. Algorithms doi: 10.1023/B:NUMA.0000040056.52424.49 – volume: 189 start-page: 676 year: 2006 ident: 10.1016/j.jcp.2010.03.033_bib15 article-title: A generalization of Peaceman–Rachford fractional step method publication-title: J. Comput. Appl. Math. doi: 10.1016/j.cam.2005.05.020 – year: 2003 ident: 10.1016/j.jcp.2010.03.033_bib13 – year: 1994 ident: 10.1016/j.jcp.2010.03.033_bib18 – volume: 36 start-page: 1414 year: 1999 ident: 10.1016/j.jcp.2010.03.033_bib4 article-title: An orthogonal spline collocation alternating direction implicit Crank–Nicolson method for linear parabolic problems on rectangles publication-title: SIAM J. Numer. Anal. doi: 10.1137/S0036142997310387 – volume: 13 start-page: 631 year: 1992 ident: 10.1016/j.jcp.2010.03.033_bib24 article-title: BI-CGSTAB: a fast and smoothly converging variant of BI-CG for the solution of nonsymmetric linear systems publication-title: SIAM J. Sci. Stat. Comput. doi: 10.1137/0913035 – volume: 7 start-page: 575 year: 1970 ident: 10.1016/j.jcp.2010.03.033_bib10 article-title: Galerkin methods for parabolic equations publication-title: SIAM J. Numer. Anal. doi: 10.1137/0707048 – volume: 16 start-page: 503 year: 1979 ident: 10.1016/j.jcp.2010.03.033_bib11 article-title: Incomplete iterations for time-stepping a Galerkin method for a quasilinear parabolic problem publication-title: SIAM J. Numer. Anal. doi: 10.1137/0716039 – volume: 12 start-page: 541 year: 1975 ident: 10.1016/j.jcp.2010.03.033_bib9 article-title: An analysis of some Galerkin schemes for the solution of nonlinear time-dependent problems publication-title: SIAM J. Numer. Anal. doi: 10.1137/0712042 – start-page: 197 year: 1990 ident: 10.1016/j.jcp.2010.03.033_bib16 article-title: Splitting and alternating direction methods doi: 10.1016/S1570-8659(05)80035-3 – volume: 227 start-page: 8588 year: 2008 ident: 10.1016/j.jcp.2010.03.033_bib7 article-title: Spectral Chebyshev–Fourier collocation for the Helmholtz and variable coefficient equations in a disk publication-title: J. Comput. Phys. doi: 10.1016/j.jcp.2008.06.009 – ident: 10.1016/j.jcp.2010.03.033_bib8 – year: 2001 ident: 10.1016/j.jcp.2010.03.033_bib20 – year: 1989 ident: 10.1016/j.jcp.2010.03.033_bib22 – volume: 73 start-page: 1801 year: 2004 ident: 10.1016/j.jcp.2010.03.033_bib1 article-title: Spectral-fractional step Runge–Kutta discretizations for initial boundary value problems with time dependent boundary conditions publication-title: Math. Comput. doi: 10.1090/S0025-5718-04-01660-6 – volume: vol. V year: 1997 ident: 10.1016/j.jcp.2010.03.033_bib2 article-title: Spectral Methods – volume: 15 start-page: 1489 year: 1994 ident: 10.1016/j.jcp.2010.03.033_bib21 article-title: Efficient spectral-Galerkin method I. Direct solvers of second- and fourth-order equations using Legendre polynomials publication-title: SIAM J. Sci. Comput. doi: 10.1137/0915089 – volume: 28 start-page: 1054 year: 2006 ident: 10.1016/j.jcp.2010.03.033_bib5 article-title: An alternating-direction implicit orthogonal spline collocation scheme for nonlinear parabolic problems on rectangular polygons publication-title: SIAM J. Sci. Comput. doi: 10.1137/050627885 – year: 1985 ident: 10.1016/j.jcp.2010.03.033_bib23 |
| SSID | ssj0008548 |
| Score | 1.9766145 |
| Snippet | We discuss the Crank–Nicolson and Laplace modified alternating direction implicit Legendre and Chebyshev spectral collocation methods for a linear, variable... We discuss the Crank-Nicolson and Laplace modified alternating direction implicit Legendre and Chebyshev spectral collocation methods for a linear, variable... |
| SourceID | proquest pascalfrancis crossref elsevier |
| SourceType | Aggregation Database Index Database Enrichment Source Publisher |
| StartPage | 5182 |
| SubjectTerms | ADI Chebyshev approximation Coefficients Collocation methods Computational techniques Crank–Nicolson Dirichlet problem Exact sciences and technology Laplace modified Legendre and Chebyshev polynomials Mathematical analysis Mathematical methods in physics Mathematical models Parabolic initial-boundary value problems Physics Spectra Spectral collocation Spectral lines |
| Title | ADI spectral collocation methods for parabolic problems |
| URI | https://dx.doi.org/10.1016/j.jcp.2010.03.033 https://www.proquest.com/docview/753752093 |
| Volume | 229 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVESC databaseName: Elsevier SD Complete Freedom Collection [SCCMFC] customDbUrl: eissn: 1090-2716 dateEnd: 99991231 omitProxy: true ssIdentifier: ssj0008548 issn: 0021-9991 databaseCode: ACRLP dateStart: 19950101 isFulltext: true titleUrlDefault: https://www.sciencedirect.com providerName: Elsevier – providerCode: PRVESC databaseName: Elsevier SD Freedom Collection Journals [SCFCJ] customDbUrl: eissn: 1090-2716 dateEnd: 99991231 omitProxy: true ssIdentifier: ssj0008548 issn: 0021-9991 databaseCode: AIKHN dateStart: 19950101 isFulltext: true titleUrlDefault: https://www.sciencedirect.com providerName: Elsevier – providerCode: PRVESC databaseName: Science Direct customDbUrl: eissn: 1090-2716 dateEnd: 99991231 omitProxy: true ssIdentifier: ssj0008548 issn: 0021-9991 databaseCode: .~1 dateStart: 19950101 isFulltext: true titleUrlDefault: https://www.sciencedirect.com providerName: Elsevier – providerCode: PRVLSH databaseName: Elsevier Journals customDbUrl: mediaType: online eissn: 1090-2716 dateEnd: 99991231 omitProxy: true ssIdentifier: ssj0008548 issn: 0021-9991 databaseCode: AKRWK dateStart: 19660801 isFulltext: true providerName: Library Specific Holdings |
| link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV07a8MwED7yWAql79L0ETR0KriRJTl2xpA2JC1kaiCbkGQFEkpi4mTtb-_JlgOhtENBky0hc9J9d7K-uwN4RCUKqTUiCBWLAnSpadCbR1GgeTcMVYr4mBZsi0l3NBVvs2hWg0EVC-NolR77S0wv0No_6XhpdrLFwsX4MhdD73KeoU1jszo00f4kSQOa_fH7aLIH5CQSJSA7NgIOqC43C5rX0mSe4MWx8d_M03GmchTavKx28QO4C2s0PIMT70aSfvml51Czqws49S4l8QqbX0LcfxmTIppyg93doq_Lf3SkLB2dE3Raicv_rV2CYOLry-RXMB2-fgxGga-VEBge9baBTqxW1vA4NWhwRMI0N7FmUcJSFiqNclHaoi2nVhglGDXMmNSVGrH4wiSUX0NjtV7ZGyCp8wKsoswKPP2hgneZQtlpBAMzN1q3gFYiksYnEnf1LD5lxRhbSpSqdFKVlGPjLXjaD8nKLBp_dRaV3OXBVpCI8n8Nax-s0X4ilyMxiXthC0i1aBJ1yF2MqJVd73KJR7bY0YH47f-mvoOjklTgWLz30NhudvYBfZWtbkP9-Sts-x35DTVi5pY |
| linkProvider | Elsevier |
| linkToHtml | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1LT8MwDLZgHEBCvBHjmQMnpLI2SdfuiAZovHbapN2iJM2kTWib6Ljy27HbdGhC7ICUU5solRN_dprPNsA1KlEUOiuDSPM4QJc6DFrDOA6MaEaRzhAfs4Jt0W12-vJ5EA_WoF3FwhCt0mN_iekFWvsnDS_Nxmw0ohhfTjH0lPMMbRofrMOGjHlCJ7Dbrx-eRxrLEo6Ji4Ddq6vNguQ1tjNP7xLYxF_GaXumcxTZsKx18Qu2C1v0uAc73olkd-V37sOamxzArncomVfX_BCSu_snVsRSfmB3WvJp-YeOlYWjc4YuK6Ps34bSAzNfXSY_gv7jQ6_dCXylhMCKuDUPTOqMdlYkmUVzI1NuhE0Mj1Oe8UgbkabaOLTkoZNWSx5abm1GhUYcvrBpKI6hNplO3AmwjHwAp0PuJJ79UL2bXKPsDEKBHVpj6hBWIlLWpxGnahbvquKLjRVKVZFUVSiwiTrcLIbMyhwaqzrLSu5qaSMoxPhVwy6X1mgxEWVITJNWVAdWLZpCDaJrET1x089c4YEtITKQOP3f1Few2em9varXp-7LGWyV9ALi855Dbf7x6S7Qa5mby2JXfgMdEOde |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=ADI+spectral+collocation+methods+for+parabolic+problems&rft.jtitle=Journal+of+computational+physics&rft.au=Bialecki%2C+B.&rft.au=de+Frutos%2C+J.&rft.date=2010-07-01&rft.issn=0021-9991&rft.volume=229&rft.issue=13&rft.spage=5182&rft.epage=5193&rft_id=info:doi/10.1016%2Fj.jcp.2010.03.033&rft.externalDBID=n%2Fa&rft.externalDocID=10_1016_j_jcp_2010_03_033 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0021-9991&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0021-9991&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0021-9991&client=summon |